Lecture 11 b Atomic Physics Nuclear Reactions Copyright

Units of Chapter 37 • Early Models of the Atom • Atomic Spectra: Key

37 -9 Early Models of the Atom It was known that atoms were electrically neutral, but that they could become charged, implying that there were positive and negative charges and that some of them could be removed. One popular atomic model was the “plum-pudding” model: Copyright © 2009 Pearson Education, Inc.

37 -9 Early Models of the Atom This model had the atom consisting of a bulk positive charge, with negative electrons buried throughout. Rutherford did an experiment that showed that the positively charged nucleus must be extremely small compared to the rest of the atom. He scattered alpha particles – helium nuclei – from a metal foil and observed the scattering angle. He found that some of the angles were far larger than the plum-pudding model would allow. Copyright © 2009 Pearson Education, Inc.

37 -9 Early Models of the Atom The only way to account for the large angles was to assume that all the positive charge was contained within a tiny volume – now we know that the radius of the nucleus is 1/10, 000 that of the atom. Copyright © 2009 Pearson Education, Inc.

37 -9 Early Models of the Atom Therefore, Rutherford’s model of the atom is

37 -10 Atomic Spectra: Key to the Structure of the Atom A very thin

37 -10 Atomic Spectra: Key to the Structure of the Atom An atomic spectrum is a line spectrum – only certain frequencies appear. If white light passes through such a gas, it absorbs at those same frequencies. Copyright © 2009 Pearson Education, Inc.

37 -10 Atomic Spectra: Key to the Structure of the Atom The wavelengths of electrons emitted from hydrogen have a regular pattern: This is called the Balmer series. R is the Rydberg constant: Copyright © 2009 Pearson Education, Inc.

37 -10 Atomic Spectra: Key to the Structure of the Atom Other series include

37 -10 Atomic Spectra: Key to the Structure of the Atom A portion of the complete spectrum of hydrogen is shown here. The lines cannot be explained by the Rutherford theory. Copyright © 2009 Pearson Education, Inc.

37 -11 The Bohr Model Bohr proposed that the possible energy states for atomic electrons were quantized – only certain values were possible. Then the spectrum could be explained as transitions from one level to another. Copyright © 2009 Pearson Education, Inc.

37 -11 The Bohr Model Bohr found that the angular momentum was quantized: .

37 -11 The Bohr Model An electron is held in orbit by the Coulomb

37 -11 The Bohr Model Using the Coulomb force, we can calculate the radii

37 -11 The Bohr Model The lowest energy level is called the ground state;

Energy Levels for Hydrogen Atom – Bohr Model Copyright © 2009 Pearson Education, Inc.

Ionization Energy Ionization energy (or binding energy) is the minimum energy required to remove an electron from an atom initially at the ground state. Example: Ionization energy for hydrogen atom is 13. 6 e. V. This is precisely the energy needed to remove an electron from the lowest state E 1 = 13. 6 e. V to E = 0 where it can be free. Copyright © 2009 Pearson Education, Inc.

37 -11 The Bohr Model Example 37 -13: Wavelength of a Lyman line. Use this figure to determine the wavelength of the first Lyman line, the transition from n = 2 to n = 1. In what region of the electromagnetic spectrum does this lie? Copyright © 2009 Pearson Education, Inc.

37 -11 The Bohr Model Example 37 -14: Wavelength of a Balmer line. Determine the wavelength of light emitted when a hydrogen atom makes a transition from the n = 6 to the n = 2 energy level according to the Bohr model. Copyright © 2009 Pearson Education, Inc.

37 -11 The Bohr Model Example 37 -15: Absorption wavelength. Use this figure to determine the maximum wavelength that hydrogen in its ground state can absorb. What would be the next smaller wavelength that would work? Copyright © 2009 Pearson Education, Inc.

Summary of Chapter 37 • Rutherford showed that atom has tiny nucleus. • Line spectra are explained by electrons having only certain specific orbits. • Ground state has the lowest energy; the others are called excited states. Copyright © 2009 Pearson Education, Inc.

X-ray Production by X-ray tube (Giancoli Chp. 35 p. 938) Electrons emitted by a heated filament in a vacuum tube are accelerated by a high voltage. When they strike the surface of the anode, the ‘target’, X-rays are emitted. Copyright © 2009 Pearson Education, Inc.

X-ray Spectrum (Giancoli Chp. 39 p. 1055) Spectrum of X-ray emitted from a molybdenum target in an X-ray tube operated at 50 k. V. The spectrum consists of the continuous part (with cutoff o) and the discrete part (characteristic peaks) Copyright © 2009 Pearson Education, Inc.

$35 -10 X-Rays and X-Ray Diffraction The wavelengths of X-rays are very short. Diffraction$

35 -10 X-Rays and X-Ray Diffraction The wavelengths of X-rays are very short. Diffraction experiments are impossible to do with conventional diffraction gratings. Crystals have spacing between their layers that is ideal for diffracting X-rays.

$X-ray Diffraction (Giancoli p. 939) Bragg equation for constructive interference: 2 d sin =$

X-ray Diffraction (Giancoli p. 939) Bragg equation for constructive interference: 2 d sin = m m = 1, 2, 3, … d = the spacing between two adjacent plane of the crystal f = the angle between the X-ray & the plane of the crystal (grazing angle) = wavelength of the X-ray Copyright © 2009 Pearson Education, Inc.

Units of Chapter 42 • Nuclear Reactions and the Transmutation of Elements • Nuclear Fission • Nuclear Fusion

42. 1 Nuclear Reactions and the Transmutation of Elements A nuclear reaction is the process in which a nucleus is struck by another nucleus or particle transforming the original nucleus into another nucleus. If the original nucleus is transformed into another, this is called transmutation. An example:

42. 1 Nuclear Reactions and the Transmutation of Elements Energy and momentum must be conserved in nuclear reactions. Generic reaction: The reaction energy, or Q-value, is the sum of the initial masses less the sum of the final masses, multiplied by c 2:

Nuclear Fission A massive nucleus splits into fragments, releasing energy in the process. Copyright

42. 3 Nuclear Fission Example: After absorbing a neutron, a uranium-235 nucleus will split into two roughly equal parts. One way to visualize this is to view the nucleus as a kind of liquid drop.

42. 3 Nuclear Fission Conceptual Example 42 -5: Counting nucleons. Identify the element X in the fission reaction

42. 4 Nuclear Fusion Two small nuclei fuse together to form a larger nucleus, releasing energy in the process. Example 42 -7: Fusion energy release. One of the simplest fusion reactions involves the production of deuterium, from a neutron and a proton: ,

42. 4 Nuclear Fusion The Sun creates power by fusing hydrogen into helium through the following set of reactions: